Now that's a bug right there! Not showing a saving throw occurring/happening.
So, what it sounds like happened is you used Animal Friendship, the Deep Rothe passed it's saving throw, but the screen did not show a saving throw was being done, the beast became hostile. With the bug being no saving throw being made was shown.
I now feel like I should test this on all animals in the game... >.>
So, I just tested it on the Sacred Boar and the roll icon didn't show up, it just straight up charmed the boar. I'll be testing this further also.